Answer is C. 5 cm
Given:
AB (say) = 4 cm
Radius (OB) = 3 cm
Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.
By above property, ∆AOB is right-angled at ∠ABO.
Therefore,
By Pythagoras Theorem in ∆POQ,
OA2 = OB2 + BA2
⇒ OA= √(OB2 + BA2)
⇒ OA= √(32 + 42)
⇒ OA= √(9 + 16)
⇒ OA = √25 cm
⇒ OA = 5 cm
Hence, distance of A from center = 5 cm